Combining Symbolic Tools with Interval Analysis. An Application to Solve Robust Control Problems

Complex systems are often subjected to uncertainties that make its model difficult, if not impossi-ble to obtain. A quantitative model may be inadequate to represent the behavior of systems which require an explicit representation of imprecision and uncertainty. Assuming that the uncertainties are structured, these models can be handled with interval models in which the values of the pa-rameters are allowed to vary within numeric intervals. Robust control uses such mathematical models to explicitly have uncertainty into account. Solving robust control problems, like finding the robust stability or designing a robust controller, involves hard symbolic and numeric compu-tation. When interval models are used, it also involves interval computation. The main advantage using interval analysis is that it provides guaranteed solutions, but as drawback its use requires the interaction with multiple kinds of data. We present a methodology and a framework that com-bines symbolic and numeric computation with interval analysis to solve robust control problems